Question

`(2)/(3) -4x+(7)/(2) =-9x+(5)/(6)`

Answer 1

`\large\boxed{x=-(2)/(3)}`

Explanation:

`(2)/(3)-4x+(7)/(2)=-9x+(5)/(6)\qquad\text{multiply both sides by LCD = 6}\\\\6\!\!\!\!\diagup^2\cdot(2)/(3\!\!\!\!\diagup_1)-(6)(4x)+6\!\!\!\!\diagup^3\cdot(7)/(2\!\!\!\!\diagup_1)=(6)(-9x)+6\!\!\!\!\diagup^1\cdot(5)/(6\!\!\!\!\diagup_1)\\\\(2)(2)-24x+(3)(7)=-54x+(1)(5)\\\\4-24x+21=-54x+5\qquad\text{combine like terms}\\\\(4+21)-24x=-54x+5\\\\25-24x=-54x+5\qquad\text{subtract 25 from both sides}\\\\25-25-24x=-54x+5-25`

`-24x=-54x-20\qquad\text{add}\ 54x\ \text{to both sides}\\\\-24x+54x=-54x+54x-20\\\\30x=-20\qquad\text{divide both sides by 30}\\\\(30x)/(30)=(-20)/(30)\\\\x=-(2)/(3)`